# Tutor profile: Niki Lee M.

## Questions

### Subject: Geometry

Given a parralelogram starting in the top left corner with point A and going clockwise to B, C, and D, the side AD and BC are the shorter sides with a length of 3.3 inches. The width of the parallelogram is 7.4 inches. Angle A is 121.5 degrees and Angle D is 58.5 degrees. What is the Area of the parallelogram?

To find the area of a parallelogram, you must know that the equation is A = width x height. To find height, you must use sin, cos, tan to find h. Since we are given the length of the hypotenuse (3.3 in) and angle of 58.5 degrees, we can use sine to find the opposite side (the height). Sin58.5 = opposite/ 3.3 The height (opposite) is 2.81 inches. To find the area we multiply the height of 2.81 inches by the width of 7.4 inches to get 20.8 square inches.

### Subject: Calculus

$$\lim _{x\to \infty \:}\left(\frac{x^5-4x^3}{2x^4}\right)=\infty $$

1. Separate equation and factor out 1/2 $$x^5/2x^4-4x^3/2x^4$$ = 1/2 $$(x^5/x^4-4x^3/x^4)$$ 2. Combine again and write 1/2 outside of limit 1/2 $$\lim _{x\to \infty \:\:}$$ $$(x^5-4x^3)/(x^4)$$ 3. Simplify by removing $$x^3$$ from the denominator $$x^5/x^3$$ = $$x^2$$ and $$-4x^3/x^3$$ = -4 4. So far we have, $$(x^2-4)/x$$ When it is just a subtraction left, we can separate the equation and find the limit of each part $$\frac{1}{2}\left(\lim _{x\to \infty \:}\left(x\right)-\lim _{x\to \infty \:}\left(\frac{4}{x}\right)\right)$$ 5. Simplify to get 1/2 ($$ \infty \:$$ - 0) 6. ^ 1/2 of $$\infty \:$$ is $$\infty \:$$ and 1/2 of zero is zero so the answer is $$\infty \:$$

### Subject: Algebra

Simplify: $$((4x^7y^3)/(3xy^4)) (5x^2/y)$$

Part 1) Simplify the part in which can be simplified $$(4x^7y^3)/(3xy^4)$$ = ($$4x^6/3y) $$ Part 2) Multiply the top half $$(4x^6) (5x^2) $$=$$20x^8$$ Part 3) Multiply the bottom half (3y) (y) = $$3y^2$$ Part 4) combine part 2 and 3 $$20x^8/3y^2$$

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